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Anderson-Darling statistic

The Anderson-Darling statistic is a measure of how far the plot points fall from the fitted line in a probability plot. The statistic is a weighted squared distance from the plot points to the fitted line with larger weights in the tails of the distribution. Minitab uses an adjusted Anderson-Darling statistic, because the statistic changes when a different plot point method is used.

Formula

Notation

fitted estimate of the cumulative distribution function for the ith point

Fn(zi)

the point plotted for the ith data point

z0

equals 0

Fn(z0)

equals 0

lnn(z0)

equals 0

zn+1

Pearson correlation coefficient

For least squares estimation, Minitab calculates a Pearson correlation coefficient. If the distribution fits the data well, then the plot points on a probability plot will fall on a straight line. The correlation, usually signified by r (rho), measures the strength of the linear relationship between the X and Y variables on a probability plot.